For PD plots, model-specific confidence intervals exist that rely on models with inherent variance estimators such as Bayesian additive regression trees [1]}, [2]}.
Furthermore, various applied articles contain computations of PD confidence bands [3]}, [4]}, [5]}, [6]}, [7]}, [8]}.
These approaches either quantify only the error due to Monte Carlo approximation or, when they cover model variance, they do not account for underestimation of the variance.
This demonstrates the need for a theoretical underpinning of this inferential tool for practical research.
For PFI and related approaches, multiple suggestions for confidence intervals and variance estimation are available.
Some contributions are specific to the random forest PFI [9]}, [10]}, [11]},
for which a test for null importance was proposed by [12]}.
